Postobjective optical deflector

ABSTRACT

A postobjective optical scanner comprising a polygonal optical deflector (polygonal rotating mirror) having a plurality of convex reflecting surfaces each being a curved surface other than a spherical surface or a portion of a cylindrical surface. The deflector also utilizes a pseudocylindrical lens disposed between the polygonal optical deflector and an objective surface, having a cylindrical surface having its power in the feed direction or a rotationally symmetric surface rotationally symmetric with respect to an axis of rotational symmetry parallel to the scanning direction, and a curved surface represented by a polynominal of even degree and having its power in the scanning direction. The combined performance of the correcting effects of the polygonal optical deflector and the pseudocylindrical lens corrects the curvature of image surfaces and fθ characteristics at a high accuracy.

FIELD OF THE INVENTION AND RELATED ART STATEMENT

The present invention relates to a postobjective optical scanneremploying a polygonal mirror.

The conventional laser printer or the like employs a postobjectiveoptical scanner in which light beams fall on an optical scanner afterbeing converged by a converging lens or a preobjective optical scannerin which light beams pass a converging lens after being deflected by anoptical scanner.

The preobjective optical scanner is used generally because thepreobjective optical scanner is capable of easily correcting thecurvature of image surface and fθ characteristics by a converging lensand capable of converging light beams on a plane. However, since theconverging lens must be a wide-angle lens capable of covering an angleof deflection, the preobjective optical scanner needs an expensiveconverging lens having a complex construction. Accordingly, thepostobjective optical scanner is employed when a converging lens havinga simple construction must be used.

Although the postobjective optical scanner employs a converging lenshaving a simple construction, the point of convergence, in general, ison a curved surface. Accordingly, the curvature of image surface must becorrected when the postobjective optical scanner is employed.

Japanese Patent Laid-open (Kokai) No. 61-156020 discloses anpostobjective optical scanner employing a polygonal mirror having aspherical or cylindrical reflecting surface to reduce the curvature ofimage surface. This postobjective optical scanner reduces the curvatureof image surface to a practically negligible extent, however, the postobjective optical scanner is unable to correct scanning nonlinearity andneeds electrical means for correcting scanning nonlinearity. In a laserprinter or the like, for example, a clock is varied continuously orstepwise to correct scanning nonlinearity.

OBJECT AND SUMMARY OF THE INVENTION

It is a first object of the present invention to reduce the curvature ofimage surface.

It is a second object of the present invention to improve the fθcharacteristics.

It is a third object of the present invention to employ a polygonaldeflector having reflecting surfaces having a high degree of freedom ofdesign to achieve highly accurate correction of the curvature of imagesurface and fθ characteristics.

It is a fourth object of the present invention to employ a combinationof a polygonal deflector and a correction lens to achieve highlyaccurate correction of the curvature of image surface and fθcharacteristics.

According to the present invention, a postobjective optical scannercomprises: a polygonal deflector having convex curved or cylindricalreflecting surfaces for reflecting light emitted from a light source;and a correcting lens disposed between the polygonal deflector and anobjective surface and having a cylindrical surface having power on thefeed side or a rotationally symmetric surface having an axis ofrotational symmetry parallel to the scanning direction, and a curvedsurface of an even degree having power on the scanning side.

Since the reflecting surfaces of the polygonal deflector are convex orcylindrical, the curvature of image surface can be corrected owing tothe variation of the power of the reflecting surfaces according to theangle of deflection of light beams. The flat surface of a generalcylindrical lens is replaced with a curved surface having power on thescanning side, and the other surface of the cylindrical lens is formedin a cylindrical surface or a rotationally symmetric surface having anaxis of rotational symmetry parallel to the scanning direction dependingon the required degree of accuracy of correction. Thus, the tilt of thepolygonal deflector, as well as the curvature of image surface and fθcharacteristics, can be corrected, therefore, the combination of thepolygonal deflector and the correcting lens achieves highly accuratecorrection of the curvature of image surface and fθ characteristics.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic illustration showing the disposition of apolygonal optical deflector and a correcting lens employed in apostobjective optical scanner in a first embodiment according to thepresent invention with respect to an objective surface;

FIG. 2 is a plan view of the polygonal optical deflector of FIG. 1;

FIG. 3 is a plan view of the correcting lens of FIG. 1;

FIG. 4 is a side elevation of the correcting lens of FIG. 1;

FIG. 5 is a diagram showing light beams as viewed along the z-axis of anExample 1 of the postobjective optical scanner in the first embodiment;

FIG. 6 is a diagram showing light beams as viewed along the x-axis ofthe Example 1 of the postobjective optical scanner in the firstembodiment;

FIGS. 7(a) to 7(d) are graphs showing the respective measured data ofthe curvature of scanning line, the dislocation of image surface in thefeed direction, the dislocation of image surface in the scanningdirection, and fθ error in an Example 1 of the first embodiment;

FIGS. 8(a) to 8(d), 9(a) to 9(d), 10(a) to 10(d), 11(a) to 11(d), 12(a)to 12(d) and 13(a) to 13(d) are graphs showing the respective measureddata of the curvature of scanning line, the dislocation of image surfacein the feed direction, the disloction of image surface in the scanningdirection and fθ error in Examples 2 to 7 of the first embodiment,respectively;

FIGS. 14(a) to 14(d) are graphs showing the respective measured data ofthe curvature of scanning line, the dislocation of image surface in thefeed direction, the dislocation of image surface in the scanningdirection, and fθ error in a postobjective optical scanner employing aconventional cylindrical lens;

FIG. 15 is a diagrammatic illustration showing the disposition of apolygonal optical deflector and a correcting lens employed in apostobjective optical scanner in a second embodiment according to thepresent invention with respect to an objective surface;

FIG. 16 is a plan view of the polygonal optical deflector of FIG. 15;

FIG. 17 is a diagram showing light beams as viewed along the z-axis ofan Example 1 of the postobjective optical scanner of FIG. 15;

FIG. 18 is a diagram showing light beams as viewed along the x-axis ofthe Example 1 of the postobjective optical scanner of FIG. 15;

FIGS. 19(a) to 19(d) are graphs showing the respective measured data ofthe curvature of scanning line, dislocation of image surface in the feeddirection, dislocation of image surface in the scanning direction, andfθ error in an Example 1 of the second embodiment;

FIGS. 20(a) to 20(d) are graphs showing the respective measured data ofthe curvature of scanning line, the dislocation of image surface in thefeed direction, the dislocation of image surface in the scanningdirection, and fθ error in an Example 2 of the second embodiment;

FIG. 21 is diagrammatic illustration showing the disposition of apolygonal optical deflector and a correcting lens employed in apostobjective optical scanner in a third embodiment according to thepresent invention with to an objective surface;

FIG. 22 is a plan view of the polygonal optical deflector of FIG. 21;

FIG. 23 is a diagram showing light beams as viewed along the z-axis ofan Example 1 of the postobjective optical scanner of FIG. 21;

FIG. 24 is a diagram showing light beams as viewed along the x-axis ofthe Example 1 of the postobjective optical scanner of FIG. 21;

FIGS. 25(a) to 25(d) are graphs showing the respective measure data ofthe curvature of scanning line, the dislocation of image surface in thefeed direction, the dislocation of image surface in the scanningdirection, and fθ error in the Example 1 of the third embodiment;

FIGS. 26(a) to 26(d) are graphs showing the respective measured data ofthe curvature of scanning line, the dislocation of image surface in thefeed direction, the dislocation of image surface in the scanningdirection, and fθ error in an Example 2 of the third embodiment;

FIG. 27 is a diagrammatic illustration of the disposition of a polygonaloptical scanner and a correcting lens employed in a postobjectiveoptical deflector in a fourth embodiment according to the presentinvention with respect to an objective surface;

FIG. 28 is a plan view of the polygonal optical deflector of FIG. 27;

FIG. 29 is a diagram showing light beams as viewed along the z-axis ofan Example 1 of the fourth embodiment;

FIG. 30 is a diagram showing light beams as viewed along the x-axis ofthe Example 1 of the fourth embodiment;

FIGS. 31(a) to 31(d) are graphs showing the respective measured data ofthe curvature of scanning line, the dislocation of image surface in thefeed direction, the dislocation of image surface in the scanningdirection, and fθ error in the Example 1 of the fourth embodiment;

FIGS. 32(a) to 32(d) are graphs showing the respective measured data ofthe curvature of scanning line, the dislocation of image surface in thefeed direction, the dislocation of image surface in the scanningdirection, and fθ error in an Example 2 of the fourth embodiment;

FIG. 33 is a perspective view of a postobjective optical deflector in afifth embodiment according to the present invention;

FIG. 34 is a plan view of the postobjective optical deflector of FIG.33;

FIG. 35 is a side elevation of the postobjective optical scanner of FIG.33;

FIGS. 36 and 37 are illustrations of assistance in explaining apolygonal optical deflector having cylindrical reflecting surfaces;

FIG. 38 is a sectional view of a correcting lens taken on a planeparallel to a plane swept by a scanning beam;

FIG. 39 shows graphs showing the optical characteristics of thepostobjective optical scanner of FIG. 33;

FIG. 40 is a perspective view of a postobjective optical scanner in asixth embodiment according to the present invention;

FIG. 41 is a plan view of the postobjective optical scanner of FIG. 40;

FIG. 42 is a side elevation of the postobjective optical scanner of FIG.40;

FIGS. 43 and 44 are illustrations of assistance in explaining apolygonal optical deflector having cylindrical reflecting surfaces;

FIG. 45 is a sectional view of a correcting lens taken on a planeparallel to a plane swept by a scanning beam; and

FIG. 46 shows graphs showing the optical characteristics of thepostobjective optical scanner of FIG. 40.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS First Embodiment(FIGS. 1 to 14(d)

A postobjective optical scanner in a first embodiment according to thepresent invention comprises a polygonal optical deflector 1, and acorrecting lens 3 disposed near an objective surface 2.

Referring to FIG. 2, the polygonal optical deflector 1 rotates about anaxis passing a point O, and has six reflecting surfaces 4 each being aportion of an elliptic cylinder having its center at a point O₁, a majoraxis of b in length, and minor axis of c in length.

The correcting lens 3 has a cylindrical surface 5, which is similar tothe cylindrical surface of an cylindrical lens, and a curved surface 6of higher degree expressed by 1×10⁻² x² -4×10⁻⁸ x⁴. That is, the curvedsurface 6 is a curved surface of an even degree.

An axial light beam 7 and a differential light beam 8 fall on thereflecting surface 4 of the polygonal optical deflector 1 so as toconverge on a point S₀ at a distance l from the center O of thepolygonal optical deflector 1. The axial light beam 7 and thedifferential light beam 8 reflected by the reflecting surface 4 of thepolygonal optical deflector 1 travel through the correcting lens 3 andare focused on a point S.

Parameters shown in FIG. 1 will be described hereinafter. The polygonaloptical deflector 1 has the axis of rotation passing the center Operpendicularly to a plane swept by a scanning beam. In FIG. 1, Rm isthe radius of the inscribed circle of the polygonal optical deflector 1,R is the distance between the center O and the objective surface 2, L₀is an effective scanning distance, not shown, θ is the phase of thepolygonal optical deflector 1, and y is the position of a scanning spotof the objective surface 2. When the major axis of the elliptic crosssection of the elliptic cylinder defining one of the reflecting surfaces4 of the polygonal optical deflector 1 extends toward the objectivesurface 2, the phase θ=0. When y=L₀ /2, the phase θ=θ₀. The polygonaloptical deflector turns through an angle of 60° for one scanning cycle.The parameters, namely, the distance R, the coefficients of x to thesecond power and x to the fourth power of the function defining thecurved surface of higher degree forming the curved surface 6, thethickness of the correcting lens 3, and the position of the correctinglens 3, were varied properly to optimize the curvature of scanning line,the curvature of image surface in the scanning direction, the curvatureof image surface in the feed direction and fθ characteristics. Examplesand measured results will be described hereinafter.

    ______________________________________                                        Example 1                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)              22.65625                                                 b (mm)              264.96875                                                 c (mm) (θ = 0)                                                                              105.908431                                                Point of departure (x, y, z) (mm)                                                                 (0, 100, -5)                                              (θ = 0)                                                                 Size of beam at point of                                                                          b.sub.wx = 5, b.sub.wz = 1                                departure (mm)                                                                l (mm)               2.78582442                                               Correcting Lens:                                                              Refractive index    1.5                                                       Radius (mm)          20.8610004                                               Thickness (center) (mm)                                                                           10                                                        Coefficient of x to the second power                                                              0.001 (mm.sup.-1)                                         Coefficient of x to the fourth power                                                              -0.00000004 (mm.sup.-3)                                   Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                             (0, 300, 17.92929292)                                     Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                             (0, 352.315818, 21.3113256)                               Effective Scanning distance (mm)                                                                  220                                                       Available Angular Range of                                                                        40                                                        Reflecting Surface (deg)                                                      ______________________________________                                    

Results of the simulation are shown in FIGS. 5 (light beams as viewedalong the x-axis), 6 (light beams as viewed along the z-axis), 7(a)(curvature of scanning line), 7(b) (curvature of image surface in thefeed direction), 7(c) (curvature of image surface in the scanningdirection) and 7(d) (fθ error). The maximum curvature of scanning linewas -4.52 ×10⁻² mm, the maximum dislocation of image surface in the feeddirection was -3.083 mm, the maximum dislocation of image surface in thescanning direction was -1.524 mm, and the maximum fθ error was -4.752×10⁻² mm.

    ______________________________________                                        Example 2                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)             25                                                        b (mm)              2000                                                      c (mm)              332.925123                                                Point of departure (x, y, z) (mm)                                                                 (0, 100, -5)                                              (θ = 0)                                                                 Size of beam at point of                                                                          b.sub.wx = 5, b.sub.wz = 1                                incidence (mm)                                                                l (mm)              -0.03125                                                  Correcting Lens:                                                              Refractive index    1.5                                                       Radius (mm)         17.1405558                                                Thickness (center) (mm)                                                                           10                                                        Coefficient of x to the second power                                                              0.0024375 (mm.sup.-1)                                     Coefficient of x to the fourth power                                                              0                                                         Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                             (0, 249.625, 14.975)                                      Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                             (0, 293.300425, 17.886695)                                Effective Scanning Distance (mm)                                                                  220                                                       Available Angular Range of                                                                        40                                                        Reflecting Surface (deg)                                                      ______________________________________                                    

The paths of the light beams are similar to those shown in FIGS. 5 and6. Results of simulation are shown in FIGS. 8(a) to 8(d) correspondingto FIGS. 7(a) to 7(d), respectively.

The maximum curvature of scanning line was -6.425 μm, the maximumdislocation of image surface in the feed direction was -0.9797 mm, themaximum dislocation of image surface in the scanning direction was-3.936 mm, and the maximum fθ error was -0.2996 mm.

    ______________________________________                                        Example 3                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)             25                                                        b (mm)              2000                                                      c (mm)              332.925123                                                Point of departure (x, y, z) (mm)                                                                 (0, 100, -5)                                              (θ = 0)                                                                 Size of beam at point of                                                                          b.sub.wx = 5, b.sub.wz = 1                                departure (mm)                                                                l (mm)                                                                        Correcting Lens:                                                              Refractive index    1.5                                                       Radius (mm)         19.8623492                                                Thickness (center)  10                                                        Coefficient of x to the second power                                                              0.002375 (mm.sup.-1)                                      Coefficient of x to the fourth power                                                              -3.59375 × 10.sup.-8 (mm.sup.-3)                    Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                             (0, 239.28125, 14.2854167)                                Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                             (0, 291.239725, 17.749315)                                Effective Scanning Distance (mm)                                                                  220                                                       Available Angular Range of                                                                        40                                                        Reflecting Surface (deg)                                                      ______________________________________                                    

Results of the simulation are shown in FIG. 9(a) (curvature of scanningline), 9(b) (curvature of image surface in the feed direction), 9(c)(curvature of image surface in the scanning direction) and 9(d) (fθerror). The maximum curvature of scanning line was -5.6697×10⁻² mm, themaximum dislocation of image surface in the feed direction was -3.1609mm, the maximum dislocation of image surface in the scanning directionwas -4.0604 mm, the maximum fθ error was 0.18163 mm.

    ______________________________________                                        Example 4                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)             25                                                        b (mm)              2000                                                      c (mm)              383.035349                                                Point of departure (x, y, z) (mm)                                                                 (0, 100, -5)                                              (θ = 0)                                                                 Size of beam at point of                                                                          b.sub.wx = 5, b.sub.wz = 1                                departure (mm)                                                                l (mm)              -6.2125                                                   Correcting Lens:                                                              Refractive index    1.5                                                       Radius (mm)         18.32461341                                               Thickness (center) (mm)                                                                           10                                                        Coefficient of x to the second power                                                              0.0029 (mm.sup.-1)                                        Coefficient of x to the fourth power                                                              -6.25 × 10.sup.-8 (mm.sup.-3)                       Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                             (0, 193.25, 11.2166667)                                   Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                             (0, 243.369081, 14.5579387)                               Effective Scanning Distance (mm)                                                                  220                                                       Available Angular Range of                                                                        40                                                        Reflecting Surface (deg)                                                      ______________________________________                                    

Results of the simulation are shown in FIGS. 10(a) (curvature ofscanning line), 10(b) (curvature of image surface in the feeddirection), 10(c) (curvature of image surface in the scanningdirection), and 10(d) (fθ error). The maximum curvature of scanning linewas -0.1452 mm, the maximum dislocation of image surface in the feeddirection was -5.048 mm, the maximum dislocation of image surface in thescanning direction was 1.823 mm, and the maximum fθ error was 0.4364 mm.

    ______________________________________                                        Example 5                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)             25                                                        b (mm)              2000                                                      c (mm)              383.035349                                                Point of departure (x, y, z) (mm)                                                                 (0, 100, -5)                                              (θ = 0)                                                                 Size of beam at point of                                                                          b.sub.wx = 5, b.sub.wz = 1                                departure (mm)                                                                l (mm)              -6.146875                                                 Correcting Lens:                                                              Refractive index    1.5                                                       Radius (mm)         21.0798787                                                Thickness (center) (mm)                                                                           10                                                        Coefficient of x to the second power                                                              2.4453125 × 10.sup.-3 (mm.sup.-1)                   Coefficient of x to the fourth power                                                              -8.59375 × 10.sup.-8 (mm.sup.-3)                    Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                             (0, 182.8125, 10.5208333)                                 Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                             (0, 243.493294, 14.5662196)                               Effective Scanning Distance (mm)                                                                  220                                                       Available Angular Range of                                                                        40                                                        Reflecting Surface (deg)                                                      ______________________________________                                    

Results of the simulation are shown in FIGS. 11(a) (curvature ofscanning line), 11(b) (curvature of image surface in the feeddirection), 11(c) (curvature of image surface in the scanning direction)and 11(d) (fθ error). The maximum curvature of scanning line was -0.1855mm, the maximum dislocation of image surface in the feed direction was-9.3695 mm, the maximum dislocation of image surface in the scanningdirection was. -3.7739 mm, and the maximum fθ error was 0.3842 mm.

    ______________________________________                                        Example 6                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)             25                                                        b (mm)              2000                                                      c (mm)              383.035349                                                Point of departure (x, y, z) (mm)                                                                 (0, 100, -5)                                              (θ = 0)                                                                 Size of beam at point of                                                                          b.sub.wx = 5, b.sub.wz = 1                                departure (mm)                                                                l (mm)              -6.39375                                                  Correcting Lens:                                                              Refractive index    1.5                                                       Radius (mm)         21.875292                                                 Thickness (center) (mm)                                                                           10                                                        Coefficient of x to the second power                                                              0.001015625                                               Coefficient of x to the fourth power                                                              -0.0000001                                                Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                             (0, 200, 11.6666667)                                      Objective Surface:                                                            Center(x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                              (0, 261.48818, 15.7658787)                                Effective Scanning Distance (mm)                                                                  220                                                       Available Angular Range of                                                                        40                                                        Reflecting Surface (deg)                                                      ______________________________________                                    

Results of the simulation are shown in FIGS. 12(a) (curvature ofscanning line), 12(b) (curvature of image surface in the feeddirection), 12(c) (curvature of image surface in the scanningdirection), and 12(d) (fθ error). The maximum curvature of scanning linewas -0.20139 mm, the maximum dislocation of image surface in the feeddirection was -9.992 mm, the maximum dislocation of image surface in thescanning direction was 13.9393 mm, and the maximum fθ error was 1.0074mm.

    ______________________________________                                        Example 7                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)            16                                                         b (mm)             116.150644                                                 c (mm)             125.522999                                                 Point of departure (x, y, z) (mm)                                                                (0, 100, -5)                                               (θ = 0)                                                                 Size of beam at point of                                                                         b.sub.wx = 5, b.sub.wz = 1                                 departure (mm)                                                                l (mm)             -33.7012657                                                Correcting Lens:                                                              Refractive index   1.5                                                        Radius (mm)        14.8893078                                                 Thickness (center) (mm)                                                                          10                                                         Coefficient of x to the                                                                          1.80717663 × 10.sup.-3 (mm.sup.-1)                   second power                                                                  Coefficient of x to the                                                                          -1.59585052 × 10.sup.-7 (mm.sup.-3)                  fourth power                                                                  Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                            (0, 167.788854, 10.7653935)                                Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                            (0, 208.140537, 11.4369367)                                Effective Scanning Distance (mm)                                                                 220                                                        Available Angular Range of                                                                       40                                                         Reflecting Surface (deg)                                                      ______________________________________                                    

Results of the simulation are shown in FIGS. 13(a) (curvature ofscanning line), 13(b) (curvature of image surface in the feeddirection), 13(c) (curvature of image surface in the scanningdirection), and 13(d) (fθ error). The maximum curvature of scanning linewas 0.1038 mm, the maximum dislocation of image surface in the feeddirection was -6.9492 mm, the maximum dislocation of image surface inthe scanning direction was 3.2086 mm, and the maximum fθ error was-0.0655 mm.

REFERENCE POSTOBJECTIVE OPTICAL SCANNER

Parameters and measured results of a reference postobjective opticaldeflector provided with a polygonal optical scanner having reflectingsurfaces each formed of a portion of an elliptic cylinder, and anordinary cylindrical correcting lens will be provided hereunder.

    ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)             25                                                        b (mm)              2000                                                      c (mm)              383.035349                                                Point of departure (x, y, z) (mm)                                                                 (0, 100, -5)                                              (θ = 0)                                                                 Size of beam at point of                                                                          b.sub.wx = 5, b.sub.wz = 1                                departure (mm)                                                                l (mm)              -6.55                                                     Correcting Lens:                                                              Refractive index    1.5                                                       Radius (mm)         24.285018                                                 Thickness (center) (mm)                                                                           10                                                        Coefficient of x to the second power                                                              0 (mm.sup.-1)                                             Coefficient of x to the fourth power                                                              0 (mm.sup.-3)                                             Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                             (0, 180, 10.3333333)                                      Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                             (0, 253.833319, 15.2555546)                               Effective Scanning Distance (mm)                                                                  220                                                       Available Angular Range of                                                                        40                                                        Reflecting Surface (deg)                                                      ______________________________________                                    

Results of the simulation are shown in FIGS. 14(a), curvature ofscanning line), 14(b) (curvature of image surface in the feeddirection), 14(c) (curvature of image surface in the scanningdirection), and 14(d) (fθ error). The respective maximum values ofcurvature of scanning line, dislocation of image surface in the feeddirection, dislocation of image surface in the scanning direction, andfθ error of the reference postobjective optical scanner are considerablygreater than the respective corresponding maximum values of theforegoing examples, and the measured results proved that the correctingeffect of the correcting lens 3 of the present invention is significant.

As is apparent from the foregoing description of the postobjectiveoptical deflector in the first embodiment according to the presentinvention, since each reflecting surfaces of the polygonal opticaldeflector has two axial components and hence have a degree of freedomgreater by one than that of spherical or cylindrical reflectingsurfaces, the degree of freedom of design is increased. Since one of thesurfaces of the correcting lens employed in the postobjective opticalscanner of the present invention corresponding to the flat surface ofthe ordinary cylindrical correcting lens is formed in a curved surfaceof even degree, the tilt of the reflecting surfaces of the polygonaloptical deflector can be corrected, and thereby the combination of thepolygonal optical deflector and the pseudocylindrical correcting lenscorrects the curvature of image surface and fθ characteristics at a highaccuracy.

Second Embodiment (FIGS. 15 to 19(d)

In FIGS. 15 to 19(d), parts like or corresponding to those previouslydescribed with reference to FIGS. 1 to 14(d) are denoted by the samereference numerals or characters.

A postobjective optical scanner in a second embodiment according to thepresent invention comprises a polygonal optical deflector 1, and apseudocylindrical correcting lens 3 disposed near an objective surface2.

As shown in FIG. 16, the polygonal optical deflector 1 rotates about anaxis passing a point (center) O and perpendicular to the sheet. Thepolygonal optical deflector 1 has six reflecting surfaces 4 each formedof a portion of a hyperboloid or a hyperbolic cylinder having a contourdefined by an equation:

    (x-a-Rm).sup.2 /a.sup.2 -y.sup.2 /b.sup.2 =1

with its origin at the point O, where a and b are constants.

The pseudocylindrical correcting lens 3 has a cylindrical surface 5similar to that of the ordinary cylindrical lens, and a curved surface 6of higher degree having a contour defined by a₂ x² +a₄ x⁴ (a₂ and a₄ arecoefficients).

An axial beam 7 and a differential beam 8 fall on the reflecting surface4 of the polygonal optical deflector 1 so as to converge on a point S₀at a distance l from the center O of the polygonal optical deflector 1.The axial beam 7 and the differential beam 8 reflected by the reflectingsurface 4 are focused by the pseudocylindrical correcting lens 3 on apoint S.

Referring to FIG. 15, Rm is the radius of the inscribed circle of thecircumferential contour of the polygonal optical deflector 1, R is thedistance between the axis of rotation of the polygonal optical deflector1 and the objective surface 2, L₀, not shown, is the effective scanningdistance, θ is the phase of the polygonal optical deflector 1, and y isthe position of a scanning spot on the objective surface 2. Although theincident light beam has no direction cosine, the phase θ=0 and y=0 whenthe direction cosine of the light beam reflected by the reflectingsurface 4 of the polygonal optical deflector 1 is zero, and y=L₀ /2 whenθ=θ₀. The rotation of the polygonal optical deflector 1 through an angleof 60° corresponds to one scanning cycle. Simulated operation ofexamples of the second embodiment was performed to determine optimumvalues for the parameters including the distance R, the coefficient a₂of x to the second power, the coefficient a₄ of x to the fourth power,the thickness of the pseudocylindrical correcting lens 3 and thedisposition of the pseudocylindrical correcting lens 3 so that thecurvature of image surface in the feed direction, the curvature of imagesurface in the scanning direction, the curvature of scanning line andthe fθ characteristics are corrected appropriately.

    ______________________________________                                        Example 1                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)               16.0                                                    a (mm)                17.0768                                                 b (mm)                38.5513                                                 Point of departure (x, y, z) (mm) (θ = 0)                                                     (0, 100, -5)                                            Size of beam at point of departure (mm)                                                             b.sub.wx = 5, b.sub.wz = 1                              l (mm)                21.0430                                                 Pseudocylindrical Correcting Lens:                                            Refractive index      1.5                                                     Radius (mm)           15.7950                                                 Thickness (center) (mm)                                                                             10                                                      a.sub.2 (mm.sup.-1)   1.0620 × 10.sup.-3                                a.sub.4 (mm.sup.-3)   -9.4204 × 10.sup.-8                               Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                               (0, 228.9766, 12.9106)                                  Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                               (0, 269.3315, 15.0792)                                  Effective Scanning Distance (mm)                                                                    220                                                     Available Angular Range of Reflecting                                                               40                                                      Surface (deg)                                                                 ______________________________________                                    

FIGS. 17 and 18 show light beams in this example, as viewed in thez-axis and the x-axis, respectively.

Results of the simulation are shown in FIGS. 19(a) (curvature ofscanning line), 19(b) (curvature of image surface in the feeddirection), 19(c) (curvature of image surface in the scanningdirection), and 19(d) (fθ error). The maximum curvature of scanning linewas -0.1250 mm, the maximum curvature of image surface in the feeddirection was -4.6043 mm, the maximum curvature of image surface was-1.4320 mm, and the maximum fθ error was -2.4469×10⁻² mm.

    ______________________________________                                        Example 2                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)               24                                                      a (mm)                46.9598                                                 b (mm)                60.2560                                                 Point of departure (x, y, z) (mm) (θ = 0)                                                     (0, 100, -5)                                            Size of beam at point of departure (mm)                                                             b.sub.wx = 5, b.sub.wz = 1                              l (mm)                -9.4665                                                 Pseudocylindrical Correcting Lens:                                            Refractive index      1.5                                                     Radius (mm)           15.6868                                                 Thickness (center) (mm)                                                                             10                                                      a.sub.2 (mm.sup.-1)   4.7712 × 10.sup.-4                                a.sub.4 (mm.sup.-3)   -8.8537 × 10.sup.-8                               Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                               (0, 236.8571, 15.0194)                                  Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                               (0, 276.9392, 16.6407)                                  Effective Scanning Distance (mm)                                                                    220                                                     Available Angular Range of                                                                          40                                                      Reflecting Surface (deg)                                                      ______________________________________                                    

The paths of the light beams are similar to those shown in FIGS. 17 and18.

Results of the simulation are shown in FIGS. 20(a) (curvature ofscanning line), 20(b) (curvature of image surface in the feed direction,29(c) (curvature of image surface in the scanning direction), and 20(d)(fθ error). The maximum curvature of scanning line was 3.7581×10⁻² mm,the maximum curvature of image surface in the feed direction was -5.9444mm, the maximum curvature of image surface in the scanning direction was-2.1230 mm, and the maximum fθ error was -2.3171×10⁻² mm.

Thus, the postobjective optical scanner in the second embodimentcomprises the polygonal optical deflector having the reflecting surfaceseach formed of a portion of a convex hyperboloid or a convex hyperboliccylinder, and the pseudocylindrical correcting lens disposed between thepolygonal optical deflector and the objective surface, and having acylindrical surface having its power on the feed side, and a curvedsurface of an even degree having its power on the scanning side. Sinceeach reflecting surface of the polygonal optical deflector has two axialcomponents, the degree of freedom of the reflecting surface is greaterby one than that of a reflecting surface formed of a portion ofspherical surface or a cylindrical surface, which increases the degreeof freedom of design. Furthermore, since the surface of the correctinglens employed in the second embodiment corresponding to the flat surfaceof the ordinary correcting lens is formed of a curved surface of evendegree, the tilt of the reflecting surfaces of the polygonal opticaldeflector and the curvature of image surface can be corrected and the fθcharacteristics can be improved. Thus, the combination of the polygonaloptical deflector and the pseudocylindrical correcting lens corrects thecurvature of image surface and fθ characteristics at a high accuracy.

Third Embodiment (FIGS. 21 to 26(d))

In FIGS. 21 to 26(d), parts like or corresponding to those describedpreviously with reference to FIGS. 1 to 14(d) are denoted by the samereference numerals or characters.

A postobjective optical scanner in a third embodiment according to thepresent invention comprises a polygonal optical deflector 1, and apseudocylindrical correcting lens 3 disposed near an objective surface2.

As shown in FIG. 22, the polygonal optical deflector 1 rotates about anaxis passing a point (center) O and perpendicular to a plane swept by ascanning beam, and has six reflecting surface 4 each formed of a portionof a paraboloid or a parabolic cylinder.

The pseudocylindrical correcting lens 3 has a cylindrical surface 5similar to that of the ordinary cylindrical lens, and a curved surface 6of higher degree having a contour represented by: a₂ x² +a₄ x⁴ (a₂ anda₄ are constants). That is, the curved surface 6 is a curved surface ofeven degree.

An axial light beam 7 and a differential light beam 8 fall on thereflecting surface 4 of the polygonal optical deflector 1 so as toconverge on a point S₀ at a distance l from the center O of thepolygonal optical deflector 1. The axial light beam and the differentiallight beam 8 reflected by the reflecting surface 4 of the polygonaloptical deflector 1 travel through the correcting lens 3 and are focusedon a point S.

Parameters shown in FIG. 21 will be described hereinafter. In FIG. 21, ais the coefficient of x of the second degree, Rm is the radius of theinscribed circle of the circumferential contour of the polygonal opticaldeflector 1, R is the distance between the axis of rotation of thepolygonal optical deflector 1 and the objective surface 2, an effectivescanning distance L₀, not shown, P is the phase of the polygonal opticaldeflector 1, and y is the position of a scanning spot on the objectivesurface 2. Although the direction cosine of the incident light beam hasno x-component, the phase θ=0 and y=0 when the x-component of thedirection cosine of the reflected light beam reflected by the polygonaloptical deflector 1 is zero, and y=L₀ /2 when θ=θ₀. The polygonaloptical deflector 1 turns through an angle of 60° for one scanningcycle. Parametric simulation was performed to determine the parameters,namely, the coefficient a of second degree of the parabolic surface orparabolic cylinder forming the reflecting surfaces of the polygonaloptical deflector 1, the distance R, the coefficients of x to the secondpower and fourth power of the equation defining the curved surface 6 ofhigher degree of the pseudocylindrical correcting lens 3, the thicknessof the pseudocylindrical correcting lens 3, and the disposition of thepseudocylindrical correcting lens, to reduce the error in the linearityof the scanning line to zero. Results of parametric simulation wereevaluated in terms of curvature of image surface in the feed direction,curvature of image surface in the scanning direction, fθ characteristicsand curvature of scanning line

    ______________________________________                                        Example 1                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)               16.0                                                    a (mm.sup.-1)         3.6105 × 10.sup.-3                                Point of departure (x, y, z) (mm) (θ = 0)                                                     (0, 100, -5)                                            Size of beam at point of departure                                                                  b.sub.wx = 1, b.sub.wz = 1                              l (mm)                -34.4346                                                Pseudocylindrical Correcting Lens:                                            Refractive index      1.5                                                     Radius (mm)           14.7687                                                 Thickness (center) (mm)                                                                             10                                                      a.sub.2 (mm.sup.-1)   1.8887 × 10.sup.-3                                a.sub.4 (mm.sup.-3)   -1.5361 × 10.sup.-7                               Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                               (0, 166.5810, 10.2394)                                  Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                               (0, 206.6237, 11.3466)                                  Effective Scanning Distance (mm)                                                                    220                                                     Available Angular range of                                                                          40                                                      reflecting surface (deg)                                                      ______________________________________                                    

Results of the simulation are shown in FIGS. 23 (light beams as viewedalong the x-axis), 24 (light beams as viewed along the z-axis), 25(a)(curvature of scanning line), 25(b) (curvature of image surface in thefeed direction), 25(c) (curvature of image surface in the scanningdirection), and 25(d) (fθ error). The maximum curvature of scanning linewas -6.2888×10⁻² mm, the maximum curvature of image surface in the feeddirection was -6.6502 mm, the maximum curvature of image surface in thescanning direction was -2.26410, and the maximum fθ error was -0.1884mm.

    ______________________________________                                        Example 2                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)               16                                                      a (mm.sup.-1)         3.2623 × 10.sup.-3                                Point of departure (x, y, z) (mm) (θ = 0)                                                     (0, 100, -5)                                            Size of beam at point of departure                                                                  b.sub.wx = 1, b.sub.wz = 1                              l (mm)                -41.1647                                                Pseudocylindrical Correcting Lens:                                            Refractive index      1.5                                                     Radius (mm)           15.3892                                                 Thickness (center)    10                                                      a.sub.2 (mm.sup.-1)   1.3529 × 10.sup.-3                                a.sub.4 (mm.sup.-3)   -1.1620 × 10.sup.-7                               Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                               (0, 236.8571, 15.0194)                                  Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                               (0, 205.4683, 12.3763)                                  Effective Scanning Distance                                                                         220                                                     Available Angular Range of                                                                          40                                                      Reflecting Surface (deg)                                                      ______________________________________                                    

Paths of light beams as viewed along the z-axis and the x-axis aresimilar to those shown in FIGS. 23 and 24.

Results of the simulation are shown in FIGS. 26(a) (curvature ofscanning line), 26(b) (curvature of image surfaces in the feeddirection), 26(c) (curvature of image surface in the scanningdirection), and 26(d) (fθ error). The maximum curvature of scanning linewas 3.5940×10⁻² mm, the maximum curvature of image surface in the feeddirection was -5.0589 mm, the maximum curvature of image surface in thescanning direction was 1.8314 mm, and the maximum fθ error was-2.3171×10⁻² mm.

Since the postobjective optical scanner in the third embodimentaccording to the present invention thus comprises the polygonal opticaldeflector having reflecting surfaces for reflecting a light beam emittedfrom a light source each formed of a portion of a convex parabolicsurface of a parabolic cylinder, and the pseudocylindrical correctinglens disposed between the polygonal optical deflector and the objectivesurface, and having a cylindrical surface having power on the feed side,and a curved surface of even degree having power on the scanning side,the fθ characteristics and curvature of image surface can be correctedby the variation in the curvature of the reflecting surfaces of thepolygonal optical deflector each formed of a portion of a parabolicsurface of a parabolic cylinder and by the power in the scanningdirection of the cylindrical surface of the pseudocylindrical correctinglens. Thus, the combination of the polygonal optical deflector and thepseudocylindrical correcting lens correct the curvature of image surfaceand fθ characteristics at a high accuracy.

Fourth Embodiment (FIGS. 27 to 32(d)

A postobjective optical scanner in a fourth embodiment according to thepresent invention comprises a polygonal optical deflector 1 and apseudocylindrical correcting lens 3 disposed near an objective surface2.

The polygonal optical deflector 1 rotates about an axis passing a point(center) O perpendicularly to a plane swept by a scanning beam, and hassix reflecting surfaces 4 each formed of a curved surface of a higherdegree not less than fourth degree defined by a polynominal of evendegree.

The pseudocylindrical correcting lens 3 has a cylindrical surfacesimilar to that of the ordinary cylindrical lens and a curved surface 6of higher degree defined by a₂ x² +a₄ x⁴ (a₂ and a₄ are constants). Thatis, the curved surface 6 is a curved surface of even degree.

An axial light beam 7 and a differential light beam 8 fall on thereflecting surface 4 of the polygonal optical deflector 1 so as toconverge on a point S₀ at a distance l from the center O of thepolygonal optical deflector 1. The axial light beam 7 and thedifferential light beam 8 reflected by the reflecting surface 4 of thepolygonal optical deflector 1 travel through the pseudocylindricalcorrecting lens 3 and are focused on a point S.

Parameters shown in FIG. 27 will be described hereinafter. Coefficientsa₂, a₄ and a₆ are the coefficient respectively of a term of the seconddegree, a term of the fourth degree and a term of the sixth degree ofthe polynominal of even degree defining the shape of the polygonaloptical reflecting surfaces 4, Rm is the radius of an inscribed circleof the circumferential contour of the polygonal optical deflector 1, Ris the distance between the axis of rotation of the polygonal opticaldeflector 1 and the objective surface 2, L₀ is an effective scanningdistance, not shown, and θ is the phase of the polygonal opticaldeflector 1. Although the direction cosine of the incident light beamhas no x-component, the phase θ=0 and the position y =0 when thex-component of the direction cosine of the reflected light beamreflected by the polygonal optical deflector 1 is zero, and the phaseθ=θ₀ when y =L₀ /2. The polygonal optical deflector 1 turns through anangle of 60° for one scanning cycle. Parametric simulation was performedto determine the coefficients a₂, a₄ and a₆, the distance R, thecoefficients of x to the second power and the fourth power of anexpression representing the curved surface 6 of higher degree of thepseudocylindrical correcting lens 3, the thickness and disposition ofthe pseudocylindrical correcting lens 3 so that the effective scanningdistance is 220 mm when the available angular range of reflectingsurface is an angle of 40° and error in the linearity of the scanningline is reduced to zero. Results of the simulation were evaluated interms of curvature of scanning line, curvature of image surface in thefeed direction, curvature of image surface in the scanning direction,and fθ characteristics.

    ______________________________________                                        Example 1                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)               16.0                                                    a.sub.2 (mm.sup.-1)   3.6564 × 10.sup.-4                                a.sub.4 (mm.sup.-3)   -1.2116 × 10.sup.-9                               a.sub.6 (mm.sup.-5)   -3.4997 × 10.sup.-10                              Point of departure (x, y, z) (mm) (θ = 0)                                                     (0, 100, -5)                                            l (mm)                -34.0266                                                Pseudocylindrical Correcting Lens:                                            Refractive index      1.5                                                     Radius (mm)           14.7716                                                 Thickness (center) (mm)                                                                             10                                                      Coefficient of term of second                                                                       1.9627 × 10.sup.-3                                degree (mm.sup.-1)                                                            Coefficient of term of fourth                                                                       -1.6101 × 10.sup.-7                               degree (mm.sup.-3)                                                            Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                               (0, 167.4357, 11.3951)                                  Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                               (0, 207.4373, 11.3951)                                  Effective Scanning distance (mm)                                                                    220                                                     Available Angular Range of                                                                          40                                                      Reflecting Surface (deg)                                                      ______________________________________                                    

FIGS. 29 and 30 show light beams as viewed along the z-axis and thex-axis, respectively.

Results of the simulation are shown in FIGS. 31(a) (curvature ofscanning line), 31(b) (curvature of image surface in the feeddirection), 31(c) (curvature of image surface in the scanningdirection), and 31(d) (fθ error). The maximum curvature of scanning linewas 6.2161×10⁻² mm, the maximum curvature of image surface in the feeddirection was -6.5394 mm, the maximum curvature of image surface in thescanning direction was -2.6151 mm and the maximum fθ was -5.7676×10⁻²mm.

    ______________________________________                                        Example 2                                                                     ______________________________________                                        Polygonal Optical Deflector:                                                  Rm (mm)               24                                                      a.sub.2 (mm.sup.-1)   3.6232 × 10.sup.-3                                a.sub.4 (mm.sup.-3)   -5.3940 × 10.sup.-8                               a.sub.6 (mm.sup.-5)   -9.9994 × 10.sup.-10                              Point of departure (x, y, z) (mm) (θ = 0)                                                     (0, 100, -5)                                            l (mm)                -29.8873                                                Pseudocylindrical Correcting Lens:                                            Refractive index      1.5                                                     Radius (mm)           15.6240                                                 Thickness (center) (mm)                                                                             10                                                      Coefficient of term of second                                                                       1.0945 × 10.sup.-3                                degree (mm.sup.-1)                                                            Coefficient of term of fourth                                                                       -9.5307 × 10.sup.-8                               degree (mm.sup.-3)                                                            Vertex (x.sub.c, y.sub.c, z.sub.c) (mm) (θ = 0)                                               (0, 234.2721, 11.2107)                                  Objective Surface:                                                            Center (x.sub.s, y.sub.s, z.sub.s) (mm) (θ = 0)                                               (0, 274.3208, 16.4685)                                  Effective Scanning Distance (mm)                                                                    220                                                     Available Angular Range of                                                                          40                                                      Reflecting Surface (deg)                                                      ______________________________________                                    

Paths of light beams as viewed along the z-axis and along the x-axis aresimilar to those shown in FIGS. 29 and 30.

Results of the simulation are shown in FIGS. 32(a) (curvature ofscanning line, 32(b) (curvature of image surface in the feed direction),32(c) (curvature of image surface in the scanning direction), and 32(d)(fθ error). The maximum curvature of scanning line was 4.2962×10⁻² mm,the maximum curvature of image surface in the feed direction was -4.4578mm, the maximum curvature of image surface in the scanning direction was0.7152 mm, and the maximum fθ error was -7.0998×10⁻³ mm.

The postobjective optical scanner in the fourth embodiment comprises thepolygonal optical deflector having convex, curved reflecting surfaceseach formed of a portion of a curved surface of higher degreerepresented by a polynominal of even degree not less than fourth degree,and the pseudocylindrical correcting lens disposed between the polygonaloptical deflector and the objective surface and having a cylindricalsurface having its power on the feed side and a curved surface of evendegree having its power on the scanning side. Accordingly, thepostobjective optical scanner in the fourth embodiment according to thepresent invention has a degree of freedom of design greater than thatemploying a correcting lens having spherical or cylindrical surfaces.Furthermore, since the surface of the pseudocylindrical correcting lenscorresponding to the flat surface of the ordinary cylindrical correctinglens is formed of a portion of a curved surface of even degree, the tiltof the polygonal optical deflector can be corrected, and the curvatureof image surface and fθ characteristics can be improved. The combinationof the polygonal optical deflector and the pseudocylindrical correctinglens of the present invention achieves the correction of curvature ofimage surface and fθ characteristics at a high accuracy.

Fifth Embodiment (FIGS. 33 to 39)

Referring to FIG. 33, arranged on the same optical path are asemiconductor laser 11 serving as a light source, a collimating lens 12to collimate light beams emitted from the semiconductor laser 11, acylindrical lens 13 and a converging lens 14. A polygonal opticaldeflector 17 (polygonal rotating mirror) having a plurality ofreflecting surfaces 16 is disposed on the optical path and is mountedfixedly on the output shaft of a motor 15. Each reflecting surface 16 isformed of a portion of a spherical surface or a cylindrical surfacehaving its power (power is the refractive power or focusing power of anoptical surface) in scanning directions indicated by a double-headarrow.

A correcting lens 20 covering the angular range of a light beamreflected by the polygonal optical deflector 17 is disposed near anobjective surface 21 of a cylindrical photosensitive drum 22. Lightbeams travel through the correcting lens 20 and fall on the objectivesurface 21 of the photosensitive drum 22.

The correcting lens 20 has a surface 25 of incidence forming one of thesurfaces thereof and having its power in both the scanning direction andthe feed direction perpendicular to the scanning direction, namely, arotationally symmetric surface 24 formed of a portion of a rotationallysymmetric surface and having an axis 23 of rotational symmetry extendingin parallel to the scanning direction, and a surface 26 of departureforming the other surface thereof, having its power in the scanningdirection and symmetric with respect to an axis perpendicular to thescanning direction. The surface 26 of departure is a rotationallysymmetric curved surface 28 having an axis 27 of rotational symmetrypassing the center O₂ of a laterally symmetric shape with respect to thescanning direction and perpendicular to the axis 23 of rotationalsymmetry of the surface 25 of incidence.

Referring to FIG. 35, the distance between the circumference of thephotosensitive drum 22 and the axis 29 of rotation of the polygonaloptical deflector 17 is A, and the distance between the axis 29 ofrotation of the polygonal optical deflector 17 and the surface 25 ofincidence of the correcting lens 20 is B.

The light path on which the semiconductor laser 11, the collimating lens12, the cylindrical lens 13 and the converging lens 14 are arranged isdeclined at an angle θ=3.4° to a plane perpendicular to the reflectingsurface 16 of the polygonal optical deflector 17. The correcting lens 20and the center of the photosensitive drum 22 are located on an opticalpath inclined at the same angle θ=3.4° to the same plane perpendicularto the reflecting surface 16 of the polygonal optical deflector 17.

Light beams emitted from the semiconductor laser 11 in response to aprint signal are collimated in parallel light beams by the collimatinglens 12, travel through the cylindrical lens 13 having its power in thefeed direction, and the converging lens 14, and then fall on thereflecting surface 16 of the polygonal optical deflector 17. As thepolygonal optical deflector 17 rotates, the spot of the light beamspassed through the correcting lens 20 moves on the objective surface 21of the photosensitive drum 22 in the scanning direction for recording.

The optical geometry of the polygonal optical deflector 17 having thereflecting surfaces 16 each formed of a portion of a cylindrical surface19, the cylindrical lens 13 and the converging lens 14 will be describedhereinafter with reference to FIGS. 36 and 37. Each reflecting surface16 of the polygonal optical deflector 17 is formed of a portion of acylindrical surface having a circular cross section indicated by abroken line with a radius r and with its center at a point O. Theinscribed circle of the polygonal optical deflector 17 has a radius c(=16 mm) and has its center on the axis 29 of rotation of the polygonaloptical deflector 17. The axis 29 of rotation of the polygonal opticaldeflector 17 is parallel to the axis of the cylindrical surface passingthe point O.

The cylindrical lens 13 and the converging lens 14 are disposed so thatlight beams converge on a point S when the light beams are projected inthe direction of the axis 29 of rotation, and so that the light beamsconverge on the reflecting surface 16 when the light beams are projectedin the scanning direction. The distance between the axis 29 of rotationof the polygonal optical deflector 17 and the point S is d.

The morphology of the correcting lens 20 will be described withreference to FIG. 38 showing the correcting lens 20 in a section takenon a plane parallel to the scanning direction.

The surface 25 of incidence is formed of a portion of a rotationallysymmetric surface 24 having an axis 23 of rotational symmetry. Theradius of the surface 25 of incidence at the center O₁ thereof is e. Ona coordinate system having an origin on the center O₁, an X₁ -axisextending in the scanning direction and a Y₁ -axis extendingperpendicularly to the X₁ -axis, the contour of the section of thesurface 25 of incidence is expressed by a polynominal of degree eight:

    Y.sub.1 =α.sub.2 X.sub.1.sup.2 +α.sub.4 X.sub.1.sup.4 +α.sub.6 X.sub.1.sup.6 +α.sub.8 X.sub.1.sup.8 (1)

The surface 26 of departure is symmetric with respect to the Y₁ -axisand is formed of a portion of a rotationally symmetric surface 28 havingan axis 27 of rotational symmetry coinciding with the Y₁ -axis. On acoordinate system having an origin on a center O₂, an X₂ -axis extendingin parallel to the scanning direction and a Y₂ axis corresponding to theY₁ -axis, the contour of the section of the surface 26 of departure isexpressed by a polynominal of degree eight:

    Y.sub.2 =β.sub.2 X.sub.2.sup.2 +β.sub.4 X.sub.2.sup.4 +β.sub.6 X.sub.2.sup.6 +β.sub.8 X.sub.2.sup.8   (2)

The correcting lens 20 is formed of an acrylic resin having a refractiveindex of 1.48. The coefficients of the equations (1) and (2) will bedescribed afterward.

Computer simulation was performed to determine the parameters so thatthe fθ characteristics, the curvature of a sagittal image surface, thecurvature of a meridional image surface and the curvature of scanningline on the photosensitive drum 22 can be corrected to a practicallynegligible extent. The scanning line on the photosensitive drum 22 isliable to curve particularly in a skew incidence optical system in whichlight beams fall on the reflecting surface 16 of the polygonal opticaldeflector 17 at an angle θ to a plane perpendicular to the axis 29 ofrotation of the polygonal optical deflector 17.

Example 1

Values of the parameters selected for the computer simulation were asfollows.

    ______________________________________                                        A:  208.3 mm          B:    160.8 mm                                          r:  135.65 mm         d:    33.76 mm                                          e:  16.33 mm                                                                  α.sub.2 :                                                                   8.610 × 10.sup.-4 mm.sup.-1                                                               α.sub.4 :                                                                     4.336 × 10.sup.-9 mm.sup.-3                 α.sub.6 :                                                                   -5.509 × 10.sup.-13 mm.sup.-5                                                             α.sub.8 :                                                                     -3.071 × 10.sup.-17 mm.sup.-7               β.sub.2 :                                                                    -4.389 × 10.sup.-4 mm.sup.-1                                                              β.sub.4 :                                                                      1.616 × 10.sup.-7 mm.sup.-3                 β.sub.6 :                                                                    -6.542 × 10.sup.-13 mm.sup.-5                                                             β.sub.8 :                                                                      -2.689 × 10.sup.-18 mm.sup.-7               ______________________________________                                    

In the computer simulation, the effective scanning distance was 220 mmand the corresponding available angular range of the reflecting surface16 of the polygonal optical deflector 17 was 36°.

The curvature of scanning line, the curvature of meridional imagesurface, the curvature of sagittal image surface and fθ obtained throughthe computer simulation are shown in FIG. 39. In graphs shown in FIG.39, the vertical axes extend along the scanning direction, and thecharacteristics are measured on the horizontal axes.

    fθ Error=(Position of scanning spot on the photosensitive drum)-(Position of linear incidence)                      (3)

    Position of linear incidence=(Phase of the polygonal optical deflector)×220 mm/36°

The phase of the polygonal optical deflector 17 is zero when thepolygonal optical deflector 17 is in a position as shown in FIG. 36.

Example 2

The construction of a postobjective optical scanner is the same as thatof the postobjective optical scanner in Example 1. The values of theparameters selected for computer simulation were as follows.

    ______________________________________                                        A:  210.7 mm          B:    158.2 mm                                          r:  120.30 mm         d:    29.62 mm                                          e:  17.63 mm                                                                  α.sub.2 :                                                                   9.137 × 10.sup.-4 mm.sup.-1                                                               α.sub.4 :                                                                     7.725 × 10.sup.-3                           α.sub.6 :                                                                   -5.725 × 10.sup.-13 mm.sup.-5                                                             α.sub.8 :                                                                     -4.355 × 10.sup.-17 mm.sup.-7               β.sub.2 :                                                                    -3.586 × 10.sup.-4 mm.sup.-1                                                              β.sub.4 :                                                                      1.474 × 10.sup.-7 mm.sup.-3                 β.sub.6 :                                                                    -4.439 × 10.sup.-13 mm.sup.-5                                                             β.sub.8 :                                                                      -1.469 × 10.sup.-17 mm.sup.-7               ______________________________________                                    

The effective scanning distance was 220 mm and the correspondingavailable angular range of the reflecting surface 16 of the polygonaloptical deflector 17 was 36°.

Tabulated in Table 1 are the curvature of the sagittal image surface,the curvature of meridional image surface, linearity of fθcharacteristics and curvature of scanning line of the Examples 1 and 2of the fifth embodiment of the present invention and the examples of apostobjective optical scanner employed in a known optical scanningdevice disclosed in Japanese Patent Laid-open (Kokai) No. 61-156020,obtained through the computer simulation.

In Table 1, simulation Nos. 1, 2 and 3 are for the Examples 1, 2 and 3of the known postobjective optical scanner, respectively, and simulationNos. 4 and 5 are for the Examples 1 and 2 of the fifth embodiment of thepresent invention, respectively. In simulation Nos. 4 and 5, thelinearity is represented by the maximum value at a scanning speed in themiddle portion of the scanning line.

                  TABLE 1                                                         ______________________________________                                        Simulation No.                                                                             1       2       3     4     5                                    ______________________________________                                        Curvature of sagittal                                                                      -3.984  -4.651  -5.475                                                                              -2.709                                                                              -1.449                               image surface (mm)                                                            Curvature of -0.401  -0.788  -0.120                                                                              -0.415                                                                              0.198                                meridional                                                                    image surface (mm)                                                            Linearity (%)                                                                              -10.52  -8.26   -8.60 1.76  2.25                                 Curvature of scanning                                                                      -       -       -     0.028 0.030                                line (mm)                                                                     ______________________________________                                    

As is obvious from Table 1, the curvature of sagittal image surface andthe curvature of meridional image surface in the fifth embodiment of thepresent invention are approximately 1/2, and 1/4 to 1/5 respectively ofthose of the examples of the known postobjective optical scanner.Particularly as regards linearity, values for the fifth embodiment ofthe present invention are not more than 2 to 3%, which needs noadditional correcting means such as electrical correcting means.Furthermore, the fifth embodiment is capable of correcting the curvatureof scanning line to a practically negligible extent.

Although the Examples 1 and 2 of the fifth embodiment each is providedwith one correcting lens 20, the postobjective optical scanner may beprovided with a plurality of correcting lenses in view of variousmanufacturing conditions. For example, the correcting lens 20 may besubstituted by two lenses, namely, a first lens having the same surfaceof incidence as that of the correcting lens 20, and a spherical surfaceof departure, and a second lens having a spherical surface of incidence,and the same surface of departure as that of the correcting lens 20.

The postobjective optical deflector in the fifth embodiment according tothe present invention comprises: the polygonal optical deflector havinga plurality of reflecting surfaces each formed of a portion of aspherical surface or a cylindrical surface having its power in thescanning direction; and the correcting lens disposed between thepolygonal optical deflector and the objective surface, having arotationally symmetric curved surface of incidence having a crosssection having the shape of an arc of a circle with its center on theaxis of rotational symmetry, rotationally symmetric with respect to aplane including the axis of rotation of the polygonal optical deflectorand perpendicular to the axis of rotational symmetry and having itspower in both the scanning direction and the feed direction, and asurface of departure symmetrical with respect to a plane perpendicularto the scanning direction and having its power in the scanningdirection. Therefore, the curvature of image surface in the scanningdirection, namely, a sagittal image surface, can be corrected by formingeach reflecting surface of the polygonal optical deflector by a portionof a spherical surface of a cylindrical surface having its power in thescanning direction. Furthermore, since the surface of incidence of thecorrecting lens is formed of a rotationally symmetric curved surfacerotationally symmetric with respect to an axis of symmetry parallel tothe scanning direction, the power in the feed direction can be varied byvarying the curvature of the surface of incidence with respect to thefeed direction along the scanning direction, and thereby the curvatureof the image surface in the feed direction, namely, the meridional imagesurface, can be corrected. Still further, forming the surface ofdeparture of the correcting lens in a curved surface having its power inthe scanning direction enables the correction of fθ characteristics andthe further accurate correction of the sagittal image surface.

Thus, the curvature of the sagittal image surface, the curvature of themeridional image surface and fθ characteristics can be corrected by thecombined correcting effects of the reflecting surfaces of the polygonaloptical deflector, and the surfaces of incidence and departure of thecorrecting lens. Furthermore, the correction of fθ characteristics,which has been a significant problem, can be achieved by optical meanswithout requiring any electrical means, so that the postobjectiveoptical scanner of the present invention has high performance, and issimple in construction and inexpensive.

Sixth Embodiment (FIGS. 40 to 46) EXAMPLE 1

Referring to FIGS. 40 and 41, arranged on the same optical path are asemiconductor laser 31 serving as a light source, a collimating lens 32to collimate light beams, a cylindrical lens 33 and a converging lens34. A polygonal optical deflector (polygonal rotating mirror) 37 havinga plurality of reflecting surfaces 36 is disposed on the optical pathand is mounted fixedly on the output shaft of a motor 35. Eachreflecting surface 36 is a curved surface 38 varying in curvature fromposition to position thereon.

A correcting lens 39 is disposed so as to cover the angular range oflight beams reflected by the polygonal optical deflector 37, and acylindrical photosensitive drum 41 having an objective surface 40 onwhich light beams transmitted through the correcting lens 39 fall isdisposed behind the correcting lens 39.

The correcting lens 39 has its power (refractive power or focusingpower) in both the scanning direction indicated by a double-head arrowand the feed direction perpendicular to the scanning direction. Thecorrecting lens 39 has a surface 44 of incidence formed of a portion ofa rotationally symmetric curved surface 43 having an axis 44 of symmetryparallel to the scanning direction, and a surface 45 of departure havingits power in the scanning direction and symmetric with respect to anaxis perpendicular to the scanning direction. The surface 45 ofdeparture is formed of a portion of a rotationally symmetric curvedsurface 47 having an axis 46 of rotational symmetry passing the centerO₂ of a laterally symmetric shape with respect to the scanning directionand perpendicular to the axis 42 of rotational symmetry of the surface44 of incidence.

Referring to FIG. 42, the distance between the objective surface 40 andthe axis 48 of rotation of the polygonal optical deflector 37 is A, andthe distance between the axis 48 of rotation of the polygonal opticaldeflector 37 and the surface 44 of incidence of the correcting lens 39is B.

The light path on which the semiconductor laser 31, the collimating lens32, the cylindrical lens 33 and the converging lens 34 are arranged isdeclined at an angle θ=3.4° to a plane perpendicular to the reflectingsurface 36 of the polygonal optical deflector 37. The correcting lens 39and the center of the photosensitive drum 41 are located on an opticalpath inclined at the same angle θ=3.4° to the same plane perpendicularto the reflecting surface 36 of the polygonal optical deflector 37.

Light beams emitted from the semiconductor laser 31 in response to aprint signal are collimated in parallel light beams by the collimatinglens 32, travel through the cylindrical lens 33 having its power in thefeed direction, and the converging lens 34, and then fall on thereflecting surface 36 of the polygonal optical deflector 37. As thepolygonal optical deflector 37 rotates, the spot of the parallel lightbeams passed through the correcting lens 39 moves on the objectivesurface 40 of the photosensitive drum 41 in the scanning direction forrecording.

The optical geometry of the polygonal optical deflector 37 having thereflecting surface 36 each formed of a portion of an elliptic cylinderhaving an elliptic contour 49, the cylindrical lens 33 and theconverging lens 14 will be described hereinafter with reference to FIGS.43 and 44. The elliptic contour 49 has its center at a point O, a minoraxis of a in length, and a major axis of b in length. Each reflectingsurface 36 of the polygonal optical deflector 37 is formed of a portioncorresponding to the minor axis of a in length of the elliptic cylinder.The axis 48 of rotation of the polygonal optical deflector 37 passes thecenter of the inscribed circle having a radius of c (=16 mm) thereof andis parallel to the center axis of the elliptic cylinder passing thepoint O.

The cylindrical lens 33 and the converging lens 34 are disposed so thatlight beams converge on a point S when the light beams are projected inthe direction of the axis 48 of the polygonal optical deflector 37, andso that the light beams converge on the reflecting surface 36 of thepolygonal optical deflector 37 when the light beams are projected in thescanning direction. The distance between the axis 48 of rotation of thepolygonal optical deflector 37 and the point S is d.

The morphology of the correcting lens 39 will be described hereinafterwith reference to FIG. 45 showing the correcting lens 39 in a crosssection taken on a plane parallel to the scanning direction.

The surface 44 of incidence is formed of a portion of a rotationallysymmetric curved surface 43 having an axis 42 of rotational symmetry.The radius of the rotationally symmetric curved surface at the center O₁is e. On a coordinate system having an origin on the center O₁, an X₁-axis extending in the scanning direction and a Y₁ -axis extendingperpendicularly to the X₁ -axis, the contour of the surface 44 ofincidence 44 is expressed by a polynominal of degree eight:

    Y.sub.1 =α.sub.2 X.sub.1.sup.2 +α.sub.4 X.sub.1.sup.4 +α.sub.6 X.sub.1.sup.6 +α.sub.8 X.sub.1.sup.8 (4)

The surface 45 of departure is symmetric with respect to the Y₁ -axisand is formed of a portion of a rotationally symmetric surface 47 havingan axis 46 of rotational symmetry coinciding with the Y₁ -axis. On acoordinate system having an origin on a center O₂, an X₂ -axis extendingin parallel to the scanning direction, and a Y₂ -axis coinciding withthe Y₁ -axis, the contour of the central section of the surface 44 ofincidence is expressed by a polynominal of degree eight:

    Y.sub.2 =β.sub.2 X.sub.2.sup.2 +β.sub.4 X.sub.2.sup.4 +β.sub.6 X.sub.2.sup.6 +β.sub.8 X.sub.2.sup.8   (5)

The correcting lens 39 is formed of an acrylic resin having a refractiveindex of 1.48. The coefficients of the equations (4) and (5) will bedescribed afterward.

Computer simulation was performed to determine the parameters so thatthe fθ characteristics, the curvature of a sagittal image surface, thecurvature of a meridional image surface and the curvature of scanningline on the photosensitive drum 41 can be corrected to a practicallynegligible extent. The scanning line on the photosensitive drum 41 isliable to curve particularly in a skew incidence optical system in whichlight beams fall on the reflecting surface 36 of the polygonal opticaldeflector 37 at an angle θ, namely, an angle other than a right angle,to a plane perpendicular to the axis 29 of rotation of the polygonaloptical deflector 37. Values of the parameters selected for the computersimulation were as follows.

    ______________________________________                                        A:  208.3 mm          B:    160.8 mm                                          a:  116.15 mm         b:    125.52 mm                                         d:  33.76 mm          e:    16.33 mm                                          α.sub.2 :                                                                   8.610 × 10.sup.-4 mm.sup.-1                                                               α.sub.4 :                                                                     4.336 × 10.sup.-9 mm.sup.-3                 α.sub.6 :                                                                   -5.509 × 10.sup.-13 mm.sup.-5                                                             α.sub.8 :                                                                     -3.071 × 10.sup.-17 mm.sup.-7               β.sub.2 :                                                                    -4.389 × 10.sup.-4 mm.sup.-1                                                              β.sub.4 :                                                                      1.616 × 10.sup.-7 mm.sup.-3                 β.sub.6 :                                                                    -6.542 × 10.sup.-13 mm.sup.-5                                                             β.sub.8 :                                                                      -2.689 × 10.sup.-18 mm.sup.-7               ______________________________________                                    

In the computer simulation, the effective scanning distance was 220 mmand the corresponding available angular range of the reflecting surface36 of the polygonal optical deflector 37 was 36°.

The curvature of scanning line, the curvature of the meridional imagesurface, the curvature of the sagittal image surface and fθ errorobtained through the computer simulation are shown in FIG. 46. In graphsshown in FIG. 46, the vertical axes extend along the scanning direction,and the characteristics are measured on the horizontal axes.

    fθ Error=(Position of scanning spot on the photosensitive drum) -(Position of linear incidence)                           (6)

    Position of linear incidence=(Phase of the polygonal optical deflector)×220 mm/36°

The phase of the polygonal optical deflector 37 is zero when thepolygonal optical deflector 37 is in a position as shown in FIG. 43.

EXAMPLE 2

The construction of a postobjective optical scanner is the same as thatof the postobjective optical scanner in Example 1. The values of theparameters selected for computer simulation were as follows.

    ______________________________________                                        A:  210.7 mm          B:    158.2 mm                                          a:  68.84 mm          b:    91.00 mm                                          d:  29.62 mm          e:    17.63 mm                                          α.sub.2 :                                                                   9.137 × 10.sup.-4 mm.sup.-1                                                               α.sub.4 :                                                                     7.725 × 10.sup.-9 mm.sup.-3                 α.sub.6 :                                                                   -5.725 × 10.sup.-13                                                                       α.sub.8 :                                                                     -4.355 × 10.sup.-17 mm.sup.-7               β.sub.2 :                                                                    -3.586 × 10.sup.-4 mm.sup.-1                                                              β.sub.4 :                                                                      1.474 × 10.sup.-7 mm.sup.-3                 β.sub.6 :                                                                    -4.439 × 10.sup.-13 mm.sup.-5                                                             β.sub.8 :                                                                      -1.469 × 10.sup.-17 mm.sup.-7               ______________________________________                                    

In this example also, the effective scanning distance was 220 mm and thecorresponding available angular range of the reflecting surface 36 ofthe polygonal optical deflector 37 was 36°.

Tabulated in Table 2 are the curvature of the sagittal image surface,the curvature of the meridional image surface, the linearity of fθcharacteristics and the curvature of scanning line of the Examples 1 and2 of the sixth embodiment of the present invention and the examples of apostobjective optical scanner employed in the known optical scanningdevice disclosed in Japanese Patent Laid-open (Kokai) No. 61-156020,obtained through computer simulation.

                  TABLE 2                                                         ______________________________________                                        Simulation No.                                                                             1       2       3     4     5                                    ______________________________________                                        Curvature of sagittal                                                                      -3.984  -4.651  -5.475                                                                              -2.624                                                                              1.027                                image surface (mm)                                                            Curvature of -0.401  -0.788  -0.120                                                                              -0.415                                                                              -0.196                               meridional                                                                    image surface (mm)                                                            Linearity (%)                                                                              -10.52  -8.26   -8.60 1.76  2.23                                 Curvature of scanning                                                                      -       -       -     0.028 0.030                                line (mm)                                                                     ______________________________________                                    

In Table 2, simulation Nos. 1, 2 and 3 are for the Examples 1, 2 and 3of the known postobjective optical deflector, respectively, andsimulation Nos. 4 and 5 are for the Examples 1 and 2 of the sixthembodiment, respectively. In simulation Nos. 4 and 5, the linearity isrepresented by the maximum value at a scanning speed in the middleportion of the scanning line.

As is obvious from Table 2, the curvature of sagittal image surface andthe curvature of meridional image surface in the sixth embodiment of thepresent invention are approximately 1/2, and 1/4 to 1/5 respectively ofthose of the examples of the known postobjective optical scanner.Particularly as regards linearity, values for the sixth embodiment ofthe present invention are not more than 2 to 3%, which needs noadditional correcting means such as electrical correcting means.Furthermore, the sixth embodiment is capable of correcting the curvatureof scanning line to a practically negligible extent.

Although the Examples 1 and 2 of the sixth embodiment each is providedwith one correcting lens 39, the postobjective optical scanner may beprovided with a plurality of correcting lenses in view of variousmanufacturing conditions. For example, the correcting lens 39 may besubstituted by two lenses, namely, a first lens having the same surfaceof incidence as that of the correcting lens 39, and a spherical surfaceof departure, and a second lens having a spherical surface of incidence,and the same surface of departure as that of the correcting lens 39.

The postobjective optical scanner in the sixth embodiment according tothe present invention comprises: the polygonal optical deflector havinga plurality of reflecting surfaces each formed of a curved surfacevarying in curvature from position to position thereon; and thecorrecting lens disposed between the polygonal optical deflector and theobjective surface, having a rotationally symmetric curved surface ofincidence having a cross section having the shape of an arc of a circlewith its center on the axis of rotational symmetry, rotationallysymmetric with respect to a plane including the axis of rotation of thepolygonal optical deflector and perpendicular to the axis of rotationalsymmetry and having its power in both the scanning direction and thefeed direction, and a surface of departure symmetrical with respect to aplane perpendicular to the scanning direction and having its power inthe scanning direction. Thus, the employment of the polygonal opticaldeflector having reflecting surfaces each formed of a curved surfacevarying in curvature from position to position thereon enables thepostobjective optical scanner to correct the curvature of the imagesurface in the scanning direction, namely, the sagittal image surfacemore effectively than the postobjective optical scanner employing apolygonal optical deflector having reflecting surfaces each formed of aportion of a spherical surface or a cylindrical surface having a fixedcurvature. Furthermore, since the surface of incidence of the correctinglens is formed of a rotationally symmetric curved surface rotationallysymmetric with respect to an axis of symmetry parallel to the scanningdirection, the power in the feed direction can be varied by varying thecurvature of the surface of incidence with respect to the feed directionalong the scanning direction, and thereby the curvature of the imagesurface in the feed direction, namely, the meridional image surface canbe corrected. Still further, forming the surface of departure of thecorrecting lens in a curved surface having its power in the scanningdirection enables the correction of fθ characteristics and the furtheraccurate correction of the sagittal image surface.

Thus, the curvature of the sagittal image surface, the curvature of themeridional image surface and fθ characteristics can be corrected by thecombined correcting effects of the reflecting surfaces of the polygonaloptical deflector, and the surfaces of incidence and departure of thecorrecting lens. Furthermore, the correction of fθ characteristics,which has been a significant problem, can be achieved by optical meanswithout requiring any electrical means, so that the postobjectiveoptical scanner of the present invention has high performance, and issimple in construction and inexpensive.

What is claimed is:
 1. A postobjective optical scanner comprising:apolygonal optical deflector having a plurality of convex reflectingsurfaces for reflecting light emitted from a light source, each formedof a curved surface other than a portion of the circumference of acircular cylinder; and a pseudocylindrical lens disposed between thepolygonal optical deflector and an objective surface, and having acurved surface formed of a portion of the circumference of a circularcylinder and having its power in the feed direction, and a surfaceformed of a curved surface of even degree and having its power in thescanning direction.
 2. A postobjective optical scanner comprising:apolygonal optical deflector having a plurality of convex reflectingsurfaces for reflecting light emitted from a light source, each being aportion of an ellipsoid or an elliptic cylinder; and a pseudocylindricallens disposed between the polygonal optical deflector and an objectivesurface, and having a curved surface formed of a portion of thecircumference of a circular cylinder having its power in the feeddirection, and a curved surface of even degree having its power in thescanning direction.
 3. A postobjective optical scanner comprising:apolygonal optical deflector having a plurality of convex reflectingsurfaces for reflecting light emitted from a light source, each being aportion of a hyperboloid or a hyperbolic cylinder; and apseudocylindrical lens disposed between the polygonal optical deflectorand an objective surface, and having a curved surface formed of aportion of the circumference of a circular cylinder having its power inthe feed direction, and a curved surface of even degree having its powerin the scanning direction.
 4. A postobjective optical scannercomprising:a polygonal optical deflector having a plurality of convexreflecting surfaces for reflecting light emitted by a light source, eachbeing a portion of a paraboloid or a parabolic cylinder; and apseudocylindrical lens disposed between the polygonal optical deflectorand an objective surface, and having a curved surface formed of aportion of the circumference of a circular cylinder having its power inthe feed direction, and a curved surface of even degree having its powerin the scanning direction.